Giorgi Invexity and Optimization

1. Auflage 2008
ISBN: 978-3-540-78562-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 266 Seiten

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.

Autoren/Hrsg.

Giorgi, Giorgio

Inhaltsverzeichnis

1;Preface;7
2;Contents;9
3;1 Introduction;11
4;2 Invex Functions (The Smooth Case);21
4.1;2.1 Introduction;21
4.2;2.2 Invex Functions: De.nitions and Properties;22
4.3;2.3 Restricted Invexity and Pointwise Invexity;30
4.4;2.4 Invexity and Other Generalizations of Convexity;32
4.5;2.5 Domain and Range Transformations: The Hanson – Mond Functions;39
4.6;2.6 On the Continuity of the Kernel Function;43
5;3.-Pseudolinearity: Invexity and GeneralizedMonotonicity;49
5.1;3.1 .-Pseudolinearity;49
5.2;3.2 Invexity and Generalized Monotonicity;52
6;4 Extensions of Invexity to Nondi.erentiable Functions;61
6.1;4.1 Preinvex Functions;61
6.2;4.2 Lipschitz Invex Functions and Other Types of Nonsmooth Invex Functions;70
7;5 Invexity in Nonlinear Programming;83
7.1;5.1 Invexity in Necessary and Su.cient Optimality Conditions;83
7.2;5.2 A Su.cient Condition for Invexity Through the Use of the Linear Programming;94
7.3;5.3 Characterization of Solution Sets of a Pseudolinear Problem;97
7.4;5.4 Duality;99
7.5;5.5 Second and Higher Order Duality;110
7.6;5.6 Saddle Points, Optimality and Duality with Nonsmooth Invex Functions;113
8;6 Invex Functions in Multiobjective Programming;125
8.1;6.1 Introduction;125
8.2;6.2 Kuhn–Tucker Type Optimality Conditions;127
8.3;6.3 Duality in Vector Optimization;138
8.4;6.4 Invexity in Nonsmooth Vector Optimization;144
8.5;6.5 Nonsmooth Vector Optimization in Abstract Spaces;151
8.6;6.6 Vector Saddle Points;158
8.7;6.7 Linearization of Nonlinear Multiobjective Programming;161
8.8;6.8 Multiobjective Symmetric Duality;163
9;7 Variational and Control Problems Involving Invexity;167
9.1;7.1 Scalar Variational Problems with Invexity;167
9.2;7.2 Multiobjective Variational Problems with Invexity;178
9.3;7.3 Scalar Control Problems;205
9.4;7.4 Multiobjective Control Problems;212
10;8 Invexity for Some Special Functions and Problems;219
10.1;8.1 Invexity of Quadratic Functions;219
10.2;8.2 Invexity in Fractional Functions and Fractional Programming Problems;223
10.3;8.3 Invexity in a Class of Nondi.erentiable Problems;227
10.4;8.4 Nondi.erentiable Symmetric Duality and Invexity;247
11;References;261
12;Index;275